Upload File

overview of 3d object representations - princeton ... overview of 3d object representations thomas...

  • Home
  • Documents
  • Overview of 3D Object Representations - Princeton ... Overview of 3D Object Representations Thomas Funkhouser Princeton University C0S 597D, Fall 2003 3D Object Representations •
17
1 Overview of 3D Object Representations Thomas Funkhouser Princeton University C0S 597D, Fall 2003 3D Object Representations • What makes a good 3D object representation? Stanford and Hearn & Baker

Upload: vanlien

Post on 11-Mar-2018

229 views

Category:

Documents


3 download

Report

TRANSCRIPT

Page 1: Overview of 3D Object Representations - Princeton ... Overview of 3D Object Representations Thomas Funkhouser Princeton University C0S 597D, Fall 2003 3D Object Representations •

1

Overview of3D Object Representations

Thomas Funkhouser

Princeton University

C0S 597D, Fall 2003

3D Object Representations

• What makes a good 3D object representation?

Stanford andHearn & Baker

Page 2: Overview of 3D Object Representations - Princeton ... Overview of 3D Object Representations Thomas Funkhouser Princeton University C0S 597D, Fall 2003 3D Object Representations •

2

3D Object Representations

• What makes a good 3D object representation?� Intuitive specification� Guaranteed continuity� Guaranteed validity� Efficient rendering� Efficient boolean operations� Accurate� Concise� Structure

3D Reps for Computer Graphics

• Raw data� Point cloud� Range image� Voxels� Polygon soup

• Surfaces� Mesh� Subdivision � Parametric� Implicit

• Solids� Octree� BSP tree� CSG

• High-level structures� Scene graph

Page 3: Overview of 3D Object Representations - Princeton ... Overview of 3D Object Representations Thomas Funkhouser Princeton University C0S 597D, Fall 2003 3D Object Representations •

3

Point Cloud

• Unstructured set of 3D point samples� Acquired from range finder, computer vision, etc

Hoppe

Hoppe

Range Image

• Set of 3D points mapping to pixels of depth image� Acquired from range scanner

Brian CurlessSIGGRAPH 99 Course #4 Notes

Range Image Tesselation Range Surface

Page 4: Overview of 3D Object Representations - Princeton ... Overview of 3D Object Representations Thomas Funkhouser Princeton University C0S 597D, Fall 2003 3D Object Representations •

4

Voxels

• Uniform grid of volumetric samples� Acquired from CAT, MRI, etc.

FvDFH Figure 12.20

Stanford Graphics Laboratory

Polygon Soup

• Unstructured set of polygons� Created with interactive modeling systems?

Larson

Page 5: Overview of 3D Object Representations - Princeton ... Overview of 3D Object Representations Thomas Funkhouser Princeton University C0S 597D, Fall 2003 3D Object Representations •

5

3D Reps for Computer Graphics

• Raw data� Point cloud� Range image� Voxels� Polygon soup

• Surfaces� Mesh� Subdivision � Parametric� Implicit

• Solids� Octree� BSP tree� CSG

• High-level structures� Scene graph

Mesh

• Connected set of polygons (usually triangles)� Efficient rendering

Stanford Graphics Laboratory

Page 6: Overview of 3D Object Representations - Princeton ... Overview of 3D Object Representations Thomas Funkhouser Princeton University C0S 597D, Fall 2003 3D Object Representations •

6

Subdivision Surface

• Define surfaces as limit of refinement sequence� Guaranteed continuity, concise

Zorin & SchroederSIGGRAPH 99

Course Notes

Parametric Surface

• Tensor product spline patchs� Intuitive specification?, guaranteed continuity?,

accurate?, concise

FvDFH Figure 11.44

Page 7: Overview of 3D Object Representations - Princeton ... Overview of 3D Object Representations Thomas Funkhouser Princeton University C0S 597D, Fall 2003 3D Object Representations •

7

Implicit Surface

• Points satisfying: F(x,y,z) = 0� Guaranteed continuity, guaranteed validity, efficient

boolean operations, concise?

Polygonal Model Implicit ModelBill Lorensen

SIGGRAPH 99Course #4 Notes

3D Reps for Computer Graphics

• Raw data� Point cloud� Range image� Voxels� Polygon soup

• Surfaces� Mesh� Subdivision � Parametric� Implicit

• Solids� Octree� BSP tree� CSG

• High-level structures� Scene graph

Page 8: Overview of 3D Object Representations - Princeton ... Overview of 3D Object Representations Thomas Funkhouser Princeton University C0S 597D, Fall 2003 3D Object Representations •

8

Octree

• Binary space partition with solid cells labeled� Guaranteed validity, efficient boolean operations

FvDFH Figure 12.25

BSP Tree

• Binary space partition with solid cells labeled� Guaranteed validity, efficient boolean operations

a

b

c

d

e

f

1

2

3

7

4

5

6

a

bc

de

fg

Object

a

b

cdef

1

2

3

4

5

6

7

Binary Spatial Partition

Binary Tree

Naylor

Page 9: Overview of 3D Object Representations - Princeton ... Overview of 3D Object Representations Thomas Funkhouser Princeton University C0S 597D, Fall 2003 3D Object Representations •

9

CSG

• Hierarchy of boolean set operations (union, difference, intersect) applied to simple shapes� Intuitive specification, guaranteed validity,

efficient boolean operations

FvDFH Figure 12.27 H&B Figure 9.9

3D Reps for Computer Graphics

• Raw data� Point cloud� Range image� Voxels� Polygon soup

• Surfaces� Mesh� Subdivision � Parametric� Implicit

• Solids� Octree� BSP tree� CSG

• High-level structures� Scene graph

Page 10: Overview of 3D Object Representations - Princeton ... Overview of 3D Object Representations Thomas Funkhouser Princeton University C0S 597D, Fall 2003 3D Object Representations •

10

Scene Graph

• Union of objects at leaf nodes� Efficient rendering, high-level structure

Bell Laboratories

avalon.viewpoint.com

3D Reps for Computer Graphics

• Raw data� Point cloud� Range image� Voxels� Polygon soup

• Surfaces� Mesh� Subdivision � Parametric� Implicit

• Solids� Octree� BSP tree� CSG

• High-level structures� Scene graph

Page 11: Overview of 3D Object Representations - Princeton ... Overview of 3D Object Representations Thomas Funkhouser Princeton University C0S 597D, Fall 2003 3D Object Representations •

11

Equivalence of Representations

• Thesis:� Each fundamental representation has enough

expressive power to model the shape of any geometric object

� It is possible to perform all geometric operations with any fundamental representation!

• Analogous to Turing-Equivalence:� All computers today are turing-equivalent,

but we still have many different processors

Computational Differences

• Efficiency� Combinatorial complexity (e.g. O( n log n ) )� Space/time trade-offs (e.g. z-buffer)� Numerical accuracy/stability (degree of polynomial)

• Simplicity� Ease of acquisition� Hardware acceleration� Software creation and maintenance

• Usability� Designer interface vs. computational engine

Page 12: Overview of 3D Object Representations - Princeton ... Overview of 3D Object Representations Thomas Funkhouser Princeton University C0S 597D, Fall 2003 3D Object Representations •

12

3D Reps for Computer Graphics

• Different properties for different applications

Intuitive specification Yes NoGuaranteed continuity Yes NoGuaranteed validity Yes NoEfficient boolean operations Yes NoEfficient rendering Yes YesAccurate Yes YesConcise ? ?Structure Yes Yes

Edi

ting

Dis

play

Property

3D Reps for Analysis & Retrieval

• Different properties for different applications

Intuitive specification Yes No No NoGuaranteed continuity Yes No No NoGuaranteed validity Yes No No NoEfficient boolean operations Yes No No NoEfficient rendering Yes Yes No NoAccurate Yes Yes ? ?Concise ? ? ? YesStructure Yes Yes Yes Yes

Edi

ting

Dis

play

Ana

lysi

s

Ret

riev

al

Property

Page 13: Overview of 3D Object Representations - Princeton ... Overview of 3D Object Representations Thomas Funkhouser Princeton University C0S 597D, Fall 2003 3D Object Representations •

13

3D Reps for Analysis & Retrieval • Statistical examples

� Moments� Wavelets� Extended Gaussian Image

• Structural examples� Medial axis� Curve skeletons� Deformable models

Moments

• Define shape by moments of inertia:

• Properties� Invertible� First-order moments give center of mass� Second-order moments give principal axes of rotation

�=surface

rqppqr dxdydzzyxm

Page 14: Overview of 3D Object Representations - Princeton ... Overview of 3D Object Representations Thomas Funkhouser Princeton University C0S 597D, Fall 2003 3D Object Representations •

14

Wavelets

• Define shape with wavelet coefficients

• Properties� Invertible� Multiresolution

Jacobs, Finkelstein, & Salesin 1995

16,000 coefficients 400 coefficients 100 coefficients 20 coefficients

Extended Gaussian Image

• Define shape with histogram of normal directions� Invertible for convex objects� Spherical function

Page 15: Overview of 3D Object Representations - Princeton ... Overview of 3D Object Representations Thomas Funkhouser Princeton University C0S 597D, Fall 2003 3D Object Representations •

15

3D Reps for Analysis & Retrieval

• Statistical examples� Moments � Wavelets� Extended Gaussian Image

• Structural examples� Medial axis� Curve skeletons� Deformable models

Medial Axis

• Define shape as union of centers of maximal balls

Nina Amenta

Page 16: Overview of 3D Object Representations - Princeton ... Overview of 3D Object Representations Thomas Funkhouser Princeton University C0S 597D, Fall 2003 3D Object Representations •

16

Curve Skeleton

• Graph representing axis of local symmetry

Stanford Graphics Laboratory

Deformable Models

• Represent model as union of “part” primitives

Robert Osada

Page 17: Overview of 3D Object Representations - Princeton ... Overview of 3D Object Representations Thomas Funkhouser Princeton University C0S 597D, Fall 2003 3D Object Representations •

17

Summary

• Many possible 3D object representations� Most are “turing equivalent”� Different reps are more efficient for different tasks

• Shape analysis & retrieval� Not same requirements as modeling and rendering� We will study several different reps in this course


CG OpenGL 3D object representations-course 8

3D Object Representations for Fine-Grained Categorization€¦ · 3D Object Representations for Fine-Grained Categorization Jonathan Krause1, Michael Stark1,2, Jia Deng1, and Li Fei-Fei1

3D Object Representations for Recognition16 3DDPM Pepik et al., CVPR’12 2D detection 3D pose Occlusion 3D location • Yan et al., ICCV’07 • Hoiem et al., CVPR’07 • Liebelt

Sparse Representations for Object- and Ego-Motion

DEFINING OBJECTS - 3D REPRESENTATIONS Surface representations Polygon tables 3D curves and curved surfaces Sweep representations Constructive solid geometry

FusionNet: 3D Object Classification Using Multiple Data ...rezab/papers/fusionnet.pdfFusionNet: 3D Object Classification Using Multiple Data Representations Vishakh Hegde Matroid

Chapter 2. 3D Surface Representations

3D Object Representations (GATE-540)

Recap Object Representations

Computer Graphics 3D Object Representations. Tobias Isenberg geometry –shapes, positions –connectivity, inside/outside material properties –visuals, textures

DEFINING OBJECTS - 3D REPRESENTATIONS

3D Representations for Software Visualization

3D Object Representations for Fine-Grained Categorizationai.stanford.edu/~jkrause/papers/3drr13.pdfthese applications, 3D representations exhibit favorable per-formance due to their

3D Object Representations for Robot Perception

3D Object Representations

CA Object Representations Media 44806 Original

Manipulation action representations via tracking object ... · Manipulation action representations via tracking object-wise spatial relations Konstantinos Zampogiannis December 1,

3D Rotations and Complex Representations

Learning Object Representations for Visual Object Class

Chapter 8. Three-Dimensional Object Representations

3D object representation, Digital image matching ......measurements of physically existing objects become necessary. This paper presents a method of generating object representations

3D Object Representations for Recognition · 2020. 10. 15. · Comparison with Previous Datasets 22 #category #instance Non-centered objects Dense viewpoint 3D Shape 3D Object [1]

Overview of 3D Object Representations

Capturing the Uncertainty of Moving-Object Representations

3D Object Detection and Pose Estimation - Yu Xiang · • Hejrati & Ramanan, NIPS’12 • Fidler et al., NIPS’12 Etc. Contribution: 3D Object Representations 16 2D detection 3D

3D Object Representations - SNUvplab.snu.ac.kr/.../07_3DObjectRepresentations(ch8).pdf3D Object Representations Chapter 8 ComponentsforImageSynthesis Scenedescription Lightsource Viewpoint

3D Object Representations for Fine-Grained Categorizationvision.stanford.edu/pdf/3drr13.pdf · 2014-03-24 · 3D Object Representations for Fine-Grained Categorization Jonathan Krause1,

Computer Graphics 11: 3D Object Representations – Octrees & Fractals

RCS-603: COMPUTER GRAPHICS UNIT-III•It describes a 3D object as a set of surfaces that separates the object interior from the environment. •Space–partitioning representations

Spatial Representations of Object Locations and

1 3D Models and Matching representations for 3D object models particular matching techniques alignment-based systems appearance-based systems GC model

Explicit Occlusion Modeling for 3D Object Class ... › openaccess › content...Explicit Occlusion Modeling for 3D Object Class Representations M. Zeeshan Zia1, Michael Stark2, and

3D Object Representations for Fine-Grained Categorizationai.stanford.edu/~jkrause/papers/3drr_talk.pdfDeng, J. Krause, L. Fei-Fei. CVPR 2013. BubbleBank-3D 1. Randomly sample templates

Learning Representations for Visual Object Class Recognitionlear.inrialpes.fr/pubs/2007/MSHV07/MarszalekSchmid-VOC07... · 2007. 10. 15. · Learning Representations for Visual Object

PROTECTION OF 3D OBJECT VISUAL REPRESENTATIONS* …mark it using a robust watermarking algorithm of 3D polyg-onal lines to get protected 3D object (step 3). This water-markedobject